National Curriculum Aims:
Medium Term Planning…… Year 3 Theme 5 Geometrical Reasoning
KEY THEMATIC IDEAS: connecting the strands and meeting National Curriculum aims
Approximately 4 weeks
SIMMERING SKILLS AND ACTIVITIES within and beyond the daily maths lesson
Fluency
The main focus of this theme is develop children’s geometrical reasoning building on Year 2 Geometry
content and using a range of concrete and pictorial examples, children will develop their knowledge of 2D
and 3D shape properties and vocabulary through discussion, practical activities, visualisation, exposure to
varied orientations and model making. This knowledge will be applied in different contexts and combined
with the development of practical measurement skills such as finding perimeter and recording cm
measurements as decimals . E.g: Sam has a 2D shape with 5 equal sides, each side is 7.5 cm long. What is
the shape and what is its perimeter? Pupils will construct modelling materials, including plasticine, to
enable them to examine cross sections and identify prisms. . They will consolidate their understanding of
the relationship between turns and right angles. Using practical methods and real-life examples from their
school environment, such as “right angle finders” , children will be taught to identify right angles and
angles greater then or less than a right angle. They will be introduced to a range of geometrical vocabulary
including: horizontal, vertical, perpendicular and parallel; and should have repeated opportunities to use
this fluently in discussion and investigations. During this theme, children will have many opportunities to
meet the 3 curriculum aims, e.g. they will apply their understanding of all of the above by sorting and
classifying shapes using Venn and Carroll diagrams, justifying their reasons.
N.C.
Geometry 2D & 3D shapes/angles
Measurement—perimeter
STATUTORY
Reasoning
Draw 2-Dshapes and make 3-D shapes using modelling Measure, compare, add and subtract:
materials; recognize 3-D shapes in different orientations
lengths (m/cm/mm); mass (kg/g);
and describe them.
volume/capacity (l/ml).
Recognise angles as a property of shape or a description
of a turn.
Measure the perimeter of simple 2-D
Identify right angles, recognise that 2 right angles make shapes .
a 1/2 turn, 3 make 3/4 of a turn and 4 a complete turn;
identify whether angles are great than or less than an
angle.
NON-STATUTORY
Problem-Solving
Identify horizontal and vertical lines and pairs of perpendicular and parallel lines.
Pupil’s knowledge of the properties of shapes is extended at this stage to symmetrical and non-symmetrical
polygons & polyhedral. Pupils extend their use of the
properties of shapes. They should be able to describe
the properties of 2-D and 3-D shapes using accurate
language, including lengths of lines and acute and obtuse for angles greater and lesser than a right angle.
Pupils connect decimals and rounding to drawing and
measuring straight lines in centimetres in a variety of
contexts.
© Wandsworth & Merton Local Authorities, 2014
Pupils continue to measure using the
appropriate tools and units, progressing
to use a wider range of measures,
including comparing and using mixed
units (for example, 1 kg and 200g) and
simple equivalents of mixed units (for
example, 5m = 500cm).
 Identify and describe the properties of 3d and 2d shapes in different orientations.
 Visualise, compare and sort 2-D & 3-D shapes.
 Count from 0 in multiples of 4, 8, 50 and 100;.
 Add and subtract numbers (including measurement) mentally including a 3 digit
number and 1’s, a 3 digit number and 10’s and a 3 digit number and 100’s.
 Recognise that tenths arise from dividing an object into 10 equal parts.
 Count in tenths. Recognise and write 1/10 as 0.1
 Rounding to nearest 10 and 100.
 Recall units of measure, lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)
 Compare and use mixed units of measurement and simple equivalents of mixed
units e.g. 5m=500cm. Identify real life examples to illustrate measures used e.g.
Can of drink = 330ml, small bag of crisps = 25g
Addition and subtraction
Fractions
Add and subtract numbers mentally, including: Count up and down in tenths;
 a three-digit number and ones
recognise that tenths arise from
 a three-digit number and tens
dividing an object into 10 equal parts
 a three-digit number and hundreds
and in dividing one-digit numbers or
Add and subtract numbers with up to three
quantities by 10.
digits, using formal written methods of columnar addition and subtraction
Solve problems, including missing number
problems, using number facts, place value, and
more complex addition and subtraction.
Pupils practise solving varied addition
Pupils connect tenths to place value,
questions. For mental calculations with 2 digits decimal measures and to division by
10.
the answers could exceed 100.
Pupils use their understanding of place value
and partitioning and practise using columnar
addition with increasingly large numbers up to
3 digits to become fluent. (see Mathematics
appendix 1)
National Curriculum Aims:
Medium Term Planning
Year 3 Theme 5 : Geometrical reasoning
Approximately 4 weeks
EXEMPLAR QUESTIONS AND ACTIVITIES: connecting the strands and meeting National Curriculum aims
See Wandsworth LA Calculation Policy for more detail
on developing mental and written procedures!
KEY QUESTION ROOTS to be used and adapted in different contexts
Fluency
If I know……. then how could I work out…….? If ___ is the perimeter what could the length/width be?
Show me how you know that you are right. The perimeter is 24. how many different lengths/width can you find?
What is the same? (square/rectangle, different types of triangles) What is different? What do you notice?
All the possibilities: If this is a face what could the shape be? Show me……. (the shape /line/right angle ) These are the
properties.....what is the shape?
True or false… the longest shape always has the greatest perimeter, a 3D shape must have more than 3 flat faces, a
triangle cannot contain a right angle.
Sometimes, always, never…….a triangle has a smaller perimeter than a rectangle, a pentagon contains a right angle, a
cylinder is a prism……..
By constructing shapes with modelling
clay or plasticine, pupils can then cut
through their 3D shapes, to reveal the
2D face within. This will test whether
their 3D form is, or is not, a prism.
Pupils can also layer 2D shape models on
top of one another to construct prisms.
A prism is a solid object with:
 Identical ends
 Flat sides
 The same cross section
all along its length.
Is a cylinder a prism,
according to this
definition?
Mathsframe.co.uk
Reasoning
What are the perimeters
of these irregular shapes?
How many different
shapes can you draw with
a perimeter of 24cm?
How many different shapes can you make from
just 5 squares? What are their perimeters?
Pupils will build on prior understanding and
develop fluency by investigating shape
properties and sorting and classifying shapes,
lines and angles using Venn and Carroll diagrams.
They will revisit
symmetry and
shapes in different
orientations.
Virtual geoboard: nrich.maths.org
The work of artists such as Mondrian and Klee provide an excellent stimulus to discuss and
recognise shape, line and angle properties. using correct vocabulary.
Problem-Solving
What can you see? What else? How many right angles/
squares/rectangles? Show me a pair of parallel/
perpendicular lines.
Can you create your own Mondrian-based artwork to
include: 10 right angles?
at least 3 pairs of parallel lines?
at least 3 pairs of perpendicular lines?
2 acute angles (less than a right angle)?
2 obtuse angles (greater than a right angle)?
a line longer than half the length of your page?
a shape with a perimeter of 20cm?
a quadrilateral that is not a square or rectangle?
© Wandsworth & Merton Local Authorities, 2014
Can some of the key thematic ideas be delivered as part of a
mathematically-rich, creative topic?
Suggested ideas: STONE AGE TO IRON AGE and
Ug by Raymond Briggs
 Ug lives in a cave with a bed, clothes and many other
everyday objects made out of stones with no curved
edges. Use card or modelling equipment, such as
polydron, to construct objects only from 3D shapes with straight edges.
Describe the properties of the shapes that you have made: lines, angles,
faces, edges, shape names.
 Construct dwellings out of card or squared paper e.g. iron
age round house. What basic 3D shapes could we use to
construct this? What is the perimeter of your model’s base?
Tell me 2 ways that we could check.
 Create silhouette image of Stonehenge using dimensions given (5% of
original measurement in metres) : http://www.englishheritage.org.uk/publications/stonehenge-teachers-kit/
stonehenge-tk-activities.pdf
E.g. Sarsen Circle (upright stones) height 4m width 2.2m
÷ 2 ÷ 10: height 20cm, width 11cm
What is the perimeter of one of your tallest rectangles? What is the
perimeter of your shortest rectangle? What is the difference?
Non-routine problem: Ug wants to use sticks to create new 3D shelters
for his family. The sticks will be held in place by sticky mud. What is the
least number of sticks required to make a 3D shape? What shape are its
faces? Ug has collected 15 sticks. How many different 3D shapes can he
build using up to 15 sticks? How many faces do your shapes have? How
many sticks did you use? What do you notice?
Which rectangle has the longest
side? Which rectangle do you
think has the largest perimeter?
Why? How can we check?
Do we need to measure all
4 sides?
nrich.maths.org